visualization of buoyancy-driven …driven instabilities in porous media, for which the buoyant...

15th International Symposium on Flow VisualizationJune 25-28, 2012, Minsk, Belarus

ISFV15 – Minsk / Belarus – 2012

VISUALIZATION OF BUOYANCY-DRIVEN INSTABILITIES INREACTIVE SYSTEMS

C. Almarcha1,4,c, P. Grosfils2 , F. Dubois3, A. De Wit4

1IRPHE, UMR 7342, CNRS, Aix-Marseille Univ., 49, rue F. Joliot Curie, 13013 Marseille, France2Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles (ULB),

CP231, 1050 Brussels, Belgium.3Microgravity Research Center, Chimie Physique E.P. CP 165/62, Université Libre de Bruxelles (ULB),

Avenue F.D. Roosevelt 50, 1050 Brussels, Belgium4 Nonlinear Physical Chemistry Unit, ULB, CP231, 1050 Brussels, Belgium.

cCorresponding author: Tel.: +33413552025; Fax: +33413552001; Email: [email protected]

KEYWORDS: Main subjects: Experimental and computational fluid mechanics, reactive flows

Fluid: acid-base reactive flowsVisualization method(s): Schlieren, interferometry, particle image velocimetryOther keywords: image processing, color indicator

ABSTRACT:The study of buoyancy-driven instabilities triggered by chemical reactions has gained renewed interest

because of their implications in CO2 sequestration techniques among others. The theoretical models describing theevolution of the unstable interface between two miscible solutions, each containing a reactant, have to be compared tolaboratory-scale experiments. We expose the diverse visualization methods we used to experimentally study the relatedbuoyancy-driven instabilities of chemical fronts and their possible influence on the dynamics. This way, quantitativecomparisons with numerical simulations give good agreements.

INTRODUCTION:Chemical reactions and buoyancy-driven instabilities can often interplay in fluid dynamics. For instance, in

the specific case of CO2 sequestration in the ground or in aquifers, chemical reactions induce changes in the propertiesof the fluids (changes in the density or in the viscosity), or eventually in the properties of the porous medium (changesin the porosity). In turn, related hydrodynamic instabilities change the mixing of reactants and the yield of the reaction.

We present here the techniques to use or to avoid when experimentally studying the dynamics resulting from thecoupling between chemical reactions and hydrodynamic instabilities. More specifically, we focus here on buoyancy-driven instabilities in porous media, for which the buoyant flows are of particular importance for mixing in the absenceof any external forcing flow. Therefore, we use a Hele-Shaw cell (Figure 1 left), i.e. two glass plates separated by a thingap width, that allows quantitative comparisons with two-dimensional numerical models of porous media. Twomiscible solutions, each containing a reactant A or B, are put into contact, one above the other [1]. By diffusion andconvection, species A and B meet and the reaction A+B→C produces species C (Figure 1 right). The buoyancy-driveninstabilities result from the gradients of density in the gravity field. In the absence of reaction, three types of instabilitycan appear [2]. The Rayleigh-Taylor instability (RT) is known to appear when a denser fluid is put on top of a lessdense one. Double-diffusive (DD) fingering and diffusive layer convection (DLC) instabilities develop when the uppersolute and the lower solute diffuse at different rates. In presence of reactions, the number of possible scenarios increasesup to 32. To tackle and analyze these various cases, experimental investigation is necessary. In order to get a maximumof quantitative results, visualizations techniques must be accurate. We emphasize this with the example of an acid basereaction between HCl and NaOH solutions [3-7].



1. EXPERIMENTAL SYSTEM:

The experiments are performed in a vertically oriented Hele-Shaw cell specifically designed to create a planar interfacebetween two solutions [1]. The gap width is typically 0.5mm. The upper layer is filled from a hole made on top of thecell, and the bottom layer is filled from a hole at the bottom of the cell (in green on Figure 1). Two exhaust holes aresituated on the middle right and middle left of the cell (in red on Figure 1). They aim at evacuating the excess of liquid,and at defining the initial condition of a flat interface between the two reactants. This is done by first imposing a flux ofsolution from top and bottom (arrows on Figure 1). Upper and lower solutions meet on a line along the exhaust hole andthe stagnation point in the middle of the cell. The experiment starts when the injection fluxes are stopped. We then letthe system evolve from this situation. The thickness of the initial mixing zone between the two reactants depends on theinitial flux, as a competition between advection and diffusion at the stagnation point.

The reaction chosen is the neutralization reaction between HCl and NaOH in aqueous solutions. As they are strong acidand base, they are fully dissociated in the solution. Due to electroneutrality, we consider that ions go by pair. So speciesA is chosen to be the H+/Cl- couple and species B is the Na+/OH- couple. The product C is Na+/Cl-. The reaction-diffusion evolution of the species in the absence of convection is reported on Figure 1 right.

Fig.1: Left: Sketch of the vertically oriented Hele Shaw cell filled with an upper solution (in yellow) and a lowersolution (in blue). The cell is filled through holes (in green). The excess is evacuated thanks to two exhaust holes(in red). Right: Sketch of the reaction-diffusion concentration profiles of solutes A and B at two different times.



2. VISUALISATION TECHNIQUES:

As the solutions are transparent and colorless, the first idea would be to use a color indicator to track the pHvariations and the reaction zone. Unfortunately, we show in section 2.5 that the color indicator, as a reacting species,can modify the dynamics of the system and the resulting pattern [6,7]. This is why we first present non-intrusivetechniques.

2.1 SCHLIEREN TECHNIQUE:

The variations in concentrations and temperature modify the local optical index. The contributions are0.0083 l mol-1 for HCl, 0.0098 l mol-1 for NaOH, 0.0106 l mol-1 for NaCl and 0.001 K-1 for temperature (from ref. 8).As a consequence, we used a Toepler’s single-field-lens schlieren arrangement [9]. The knive edge was put horizontal,to vizualise the gradients in the vertical direction. An example for a molar solution of HCl on top of a molar solution ofNaOH is reported on Fig. 2. We clearly see the emergence of fingers, as an evidence of convection, in the upper layeronly [3,4]. The reaction front, i.e. the zone of coexistence of reactants, is visible as a thin flat horizontal line separatingon the bottom the dark and white zones.

Fig.2: Visualization of the pattern induced by putting a 1M HCl solution on top of 1M NaOH solution. The fieldof view is 24 mm large.

2.3 INTERFEROMETRY:

In order to get a more quantitative description of the pattern, we use a Mach-Zehnder interferometer (Fig.3)[3,10]. The source is a 633 nm Laser beam. The image is recorded by a CCD camera. An example of interferogram, attwo different times, is reported on Figure 4. The fringes, vertical in a homogeneous medium, are shifted by therefractive index variations. The demodulation by a Fourier transform algorithm [11] leads to the variations of therefractive index reported on figure 5. The absolute value of the refractive index has been fixed on the upper solutionaccording to values found in ref. 5.



Fig.3: Mach-Zehnder interferometer set-up. In the center, the Hele Shaw cell, alternatively illuminated by the white ledfor PIV measurements.

Fig.4: Interferograms at the beginning of the experiments (left) and after fingers are developed (right). The fieldof view is 8 mm large.



Fig.5: Refractive index map, reconstructed from the interferogram in Figure 4. The PIV vector field is alsoreported. The field of view is 8 mm large.

2.4 PIV TECHNIQUE:In alternance with the interferometry measure, we seeded the solution with 5 microns latex particules and

illuminated in volume with a white led. The images have been recorded on the same camera as the interferogram (seefig. 6). This way, we obtained the PIV and interferograms at the same times. The velocity field has been calculatedusing the free software DPIVsoft [12]. On figure 5, the velocity field has been superimposed on the optical index map.

Fig.6: The solutions are seeded with 5 microns latex particules. The field of view is 8 mm large.



2.5 USE OF COLOR INDICATOR:In order to visualize the reaction front in a direct way, color indicators are often used. Unfortunately, this

technique is risky because the color indicator is a chemical reactant that can interfer with the other species andcontribute to modify the density profile. As an example, in the work reported on ref. 6 and 7, Green Bromocresol wasused. The acidic form of this color indicator is yellow while its basic form is blue. The interplay of this color indicatorwith the HCl-NaOH reaction can modify the acid-base equilibrium and perturb the concentrations and density gradients.Hence, as the acidic and basic forms of the color indicator don't have the same solutal expansion coefficient, buoyancy-driven instabilities can appear just because of the presence of the color indicator. On figure 7, we reproduced theexperiment of the contact between HCl and NaOH 0.01M solutions but in the presence of 0.01M Green Bromocresol.Althought the zone of pH transition is visible (in black), we see also the emergence of fingers in the lower solution. Acomparison with Figs.2 where fingers are seen only at the top proves that the color indicator has indeed modified thedynamics. More explanations on the influence of the color indicator can be found in Refs. 6 and 7.

Fig.7: Direct visualization of the pattern for a 0.01M HCl solution with color indicator on top of 0.01M NaOHsolution with color indicator Bromocresol Green. Fingers are observed in the lower layer as well. The field ofview is 30 mm large.

3. RESULTS AND CONCLUSION:In order to confirm the experimental results from the interferometry and PIV visualizations, we have

numerically integrated a two dimensional model for flows in porous media where Darcy's law is coupled to reaction-diffusion-convection equations for the concentration of each species [3]. The parameters in the simulations were takenfrom ref. 8. The results are reported on figure 8 for the same time and scale as in figure 5. We clearly see a goodagreement between numerical simulations and experiments. We can conclude that the interferometry and PIVtechniques are well suited to study the buoyancy-driven instabilities in Hele Shaw cells, as a model of 2D porous mediawhile the use of color indicators should be avoided.



Fig.8: Optical refractive index variations and PIV vector field obtained from direct numerical simulation. To becompared to Fig.5.

References

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visualization of buoyancy-driven …driven instabilities in porous media, for which the buoyant...

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